I had a similar or exactly the same problem:
0) I have a nintendo DS LL, bought in JP
1) turn on and have both blank screens, no response on anything
2) press power button, after few secs the sleep screen appears. Sounds and keys work normally.
3) press "home" key and, the home screen appears, but no apps, system is kind of "frozen" (key work, music is there, but no apps. Upper screen is empty.)
Switched off, pressed L+R+A+UP together with Power (had to stick a pen in my mouth to do that !) and the update screen appeared. I could connect to my wifi and update the OS. All went well, but after reset, situation was exactly the same as above.
I feel the hardware is OK. I presume there is some corruption in the system ROM/RAM that prevents the boot-OS to start. Clearly, the "sleep" and "update" routines are not corrupted so they work regularly.
If I am right, it is very disappointing that Nintendo didn't think about a factory reset key somewhere, would be nice to press a key and the boot-OS is reloaded...
GR